00:01
The objective of this problem is to determine a formula that describes all primitive pithoccurant triple.
00:13
It is given that c is equal to a plus 2 where a, b, c are pithoccurant triples.
00:31
We know that pitoccurrant theorem states that a square plus b square is equal to c squared where c is the hypotenous of the right angle triangle.
00:49
Now let's substitute c is equal to a plus 2 in this expression.
00:55
So we will have a square plus b square is equal to a plus 2 the whole square, which is equal to if we expand this expression using the formula, a plus b the whole square is equal to a square plus 2av plus b square.
01:12
We will get a square plus 4a plus 2 square which is 4 now we can cancel out these two a square so we'll have b square is equal to 4 can be commonly taken out so we'll have 4 times a plus 1 from this equation what we can conclude is a plus 1 must be a perfect square.
01:43
So let's consider a is equal to 8, 15, 24, 35 and 48.
01:59
We can find the corresponding values of c from the equation a plus 2 is equal to c.
02:08
So, the value of c will be nothing but 8 plus 2 when a is equal to 8.
02:15
So we'll have the value of c as 10 and similarly we'll have the value of c as 17 here 26, 37 and 50 here.
02:27
And similarly, we can find the value of b also...